The condition of the resonant break-up of a gas bubble subjected to an acoustic wave in liquid

Abstract

The problem of a gas bubble break-up in liquid is considered in the conditions of the frequencies resonance of the radial and nth axially symmetric deformational mode 2:1. The nonlinear energy transfer between the modes is described using an efficient Krylov-Bogolyubov averaging technique. It is shown that the deformational mode magnitude can be some orders larger than the radial mode magnitude which is damped by the thermal, viscous and acoustic dissipation. The estimative criterion of bubble break-up is obtained in the cases of slow and fast acoustic wave start. The obtained pressure magnitudes in the wave for break-up are very small and the mechanism can have strong medical and technical applications.